On fractional derivative closures for turbulence: a critical evaluation

Turbulence modeling has traditionally relied heavily on the eddy viscosity concept relating turbulent fluxes to local gradients. Important deficiencies of the eddy viscosity concept include its inability to capture non-local and memory effects of turbulence. This has motivated recent interest in exploring how fractional derivatives (derivatives with non-integer order) may be helpful in generalizing the eddy viscosity concept to include non-local effects. Building on the speculative work of Chen (Chaos 16, 023126, 2006), a recent study by Epps & Cushman-Roisin has provided a systematic derivation for a fractional Laplacian model of the Reynolds stress. Meanwhile, unpublished work by Song & Karniadakis applies numerical optimization to determine the fractional order for a variable fractional RANS model in wall-bounded turbulence using DNS results, finding universal results across a range of Reynolds numbers. This talk will evaluate the general claims made in support of fractional turbulence modeling, the assumptions in the Epps & Cushman-Roisin derivation, as well as the relative success of results in these works, with an eye toward clarifying the promise and difficulties of such an approach to turbulence modeling.

Bio:

Dr. Perry Johnson earned his PhD in Mechanical Engineering at Johns Hopkins, and he was awarded the 2017 Corrsin-Kovasznay Outstanding Paper Award. He joined CTR as a postdoctoral scholar September 2017. His research interests include small-scale turbulence, multiphase flows, and near-wall dynamics.